Semipermutable subgroup

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In mathematics, in algebra, in the realm of group theory, a subgroup H of a finite group G is said to be semipermutable if H commutes with every subgroup K whose order is relatively prime to that of H.

Clearly, every permutable subgroup of a finite group is semipermutable. The converse, however, is not necessarily true.

[edit] External links

• The semipermutable subgroup and finite nilpotent group
• The Influence of semipermutable subgroups on the structure of finite groups